The electronic and geometrical structures of the ground and low-lying excited states of the diatomic AlX and AlX Ϫ series ͑XϭH, Li, Be, B, C, N, O, and F͒ are calculated by the coupled-cluster method with all singles and doubles and noniterative inclusion of triples using a large atomic natural orbital basis. All the ground-state AlX molecules except for AlF can attach an additional electron and form ground-state AlX Ϫ anions. The ground-state AlBe Ϫ , AlB Ϫ , AlC Ϫ , AlN Ϫ , and AlO Ϫ anions possess excited states that are stable toward autodetachment of an extra electron; AlBe Ϫ also has a second excited state. Low-lying excited states of all AlX but AlN can attach an extra electron and form anionic states that are stable with respect to their neutral ͑excited͒ parent states. The ground-state AlLi Ϫ , AlBe Ϫ , AlB Ϫ , AlN Ϫ , and AlO Ϫ anions are found to be thermodynamically more stable than their neutral parents. The most stable is AlO Ϫ , whose dissociation energy to AlϩO Ϫ is 6.4 eV. Correspondingly, AlO possesses the largest electron affinity ͑2.65 eV͒ in the series.